I have two drop down fields in the admin and I want one's values to change corresponding to the selection in the other one. What can I do? I would like to avoid AJAX calls.

Here is some sample code so that you can have a basic idea:
$menus = DataObject::get( 'BassMenu' );
if( $menus ) {
$fields->addFieldToTab( 'Root.Content.Main',
new DropdownField( 'BrowseMenuID', 'Select Browse Menu',
$menus->toDropDownMap( 'ID', 'Name' ), '', null, '' ),
'Content' );
}

$subMenuCategories = DataObject::get( 'BassMenuItem', 'ParentMenuID = '.$this->BrowseMenu()->ID );
$fields->addFieldToTab( 'Root.Content.Main',
new DropdownField( 'SubMenuID', 'Select under which sub-menu this page and sub-pages should show',
$subMenuCategories->toDropDownMap( 'ID', 'Title' )
) );

Realisitcally if you want to avoid AJAX cales you'll have to wait for the user to save the object to trigger a refresh. The only other option is to use a GroupedDropdownField that you populate with all BassMenuItems grouped by BassMenu and use some javascript to hide ones that match the the one selected in the first dropdown

I think there is a module that does populate dropdowns based on other fields, but I can't find it

Maybe you can use this module.
http://www.leftandmain.com/silverstripe-screencasts/2013/01/28/display-logic-module-for-silverstripe-3/

I have never tried it myself , so i am not 100% sure if it is what you are looking for.

Thanks for the responses guys, Sorry for the late reply was out for the weekend.

lx I cannot use that module because we're not allowed to at work :/ and we use ss 2.4

So my only option is to use ajax :/ Well was kinda expected but thanks for the info